What does it mean if classification error is equal between two networks but the MSE is different?
MSE just measures the squared difference between actual and target values. It can still correctly classify the values, but perhaps not with the same confidence - leading to a higher loss (e.g. an output of 0.77 vs 0.98 when the target is 1). In terms of which is better, I wouldn't know without the specifics of your problem. It is possible the higher loss could be more robust since it is less likely to have overfitted on the data, yet achieves the same accuracy.